Question

Solve: $x - 2y = - 1,{\kern 1pt} {\kern 1pt} {\kern 1pt} 2x - y = 7$

Answer 1

Here we are asked to solve the two equations to find the value of the variables $x$ and $y$ . Solving of equations can be done by many methods here we will use elimination method to solve the given equations. In this method, we will try to eliminate one of the unknown variables by modifying the given equation by multiplication or division. Then after eliminating one variable, we will have only one variable which can be easily solved then we will substitute the value of this solved variable to get the value of the other variable.

Complete answer:
We have the equations $x - 2y = - 1,{\kern 1pt} {\kern 1pt} {\kern 1pt} 2x - y = 7$ then,
Now let us take the LCM of the coefficients of $x$ from both the given equations,
$LCM(1,2) = 2$ then,
$2 \times (x - 2y + 1 = 0)$
$\Rightarrow 2x - 4y + 2 = 0$--------- $(1)$
$2x - y - 7 = 0$--------- ----$(2)$
Now subtracting equation $(2)$ from $(1)$ we get,
$\Rightarrow 2x - 4y + 2 - ({\kern 1pt} {\kern 1pt} {\kern 1pt} 2x - y - 7) = 0$
$\Rightarrow 2x - 4y + 2 - 2x + y + 7 = 0$
$\Rightarrow - 3y + 9 = 0$
$\Rightarrow 3y = 9$
$\Rightarrow y = 3$
Now substituting $y = 3$ in equation $(2)$ we get,
$2x - 3 - 7 = 0$
$\Rightarrow 2x - 10 = 0$
$\Rightarrow 2x = 10$
$\Rightarrow x = 5$
Therefore, the solution to the equations is $(5,3)$

Additional information:
A linear equation is nothing but an equation that is written with two variables. This equation may be a linear aggregate of those variables, and a steady can be present. Linear Equations are an extensive sort of equations altogether. There may be linear equations in one variable, linear equations in two variables, and so on. In every equation, one issue stays regular: The highest and the best diploma of all variables in the equation should be$1$ . Other than that, constants $0$ diploma variables can be there.

Note:
Things that we need to remember while doing elimination method: while modifying the given equations to eliminate one of the variables we must use only multiplication or division operation we are not supposed to do addition or subtraction, then we also give more attention in substituting the value of the variable that we found first if we substitute it in the wrong variable, we will end up getting a wrong answer.